A portfolio calculation must match each weight to the correct asset return. Vectors preserve that order; matrices combine the same inputs into several outputs, such as factor exposures. This lesson teaches the dimensions and arithmetic needed to perform both calculations. It prepares you to read covariance and NumPy array calculations.
Learning objectives. By the end of this note you should be able to:
- add vectors, multiply them by scalars and compute dot products;
- state the dimensions of a matrix and access its entries;
- multiply a matrix by a vector and check dimensional compatibility;
- rewrite simultaneous linear equations as ;
- interpret dot products and matrix products in portfolio language.
In this lesson
- Vectors are ordered collections
- Matrices encode linear transformations
- Linear systems
- A dimensional checklist
- Rows turn asset weights into factor exposures
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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